aka "Bourne" shell, written by Steve Bourne at AT&T Bell Labs for Unix V7 (1979).
Small, simple, and (originally) very few internal commands, so it called external programs for even the simplest
of tasks. It is always available on everything that looks vaguely like Unix.

The "C" shell. (Bill Joy, at Berkeley).
Many things in common
with the Bourne shell, but many enhancements to improve interactive use. The internal
commands used only in scripts are very different from "sh", and
similar (by design) to the "C" language syntax.

The "TC" shell. Freely available and based on "csh".
It has many additional features to make interactive use more convenient.

We use it as the default interactive shell for new accounts on all of our public systems.
Not many people write scripts in [t]csh.
See Csh Programming Considered Harmful by
Tom Christiansen for a discussion of problems with programming csh scripts.

The "Korn" shell, written by David Korn of AT&T Bell Labs (now AT&T Research).
Written as a major upgrade to "sh" and backwards compatible with it, but has many internal commands for the
most frequently used functions. It also incorporates many of the features from tcsh which enhance
interactive use (command line history recall etc.).

It was slow to gain acceptance because earlier versions were encumbered by AT&T licensing.
This shell is now freely available on all systems, but sometimes not installed by default on "free" Unix.
There are two major versions. ksh88 was the version incorporated into AT&T SVR4 Unix, and may still be installed
by some of the commercial Unix vendors. ksh93 added more features, primarily for programming, and better POSIX compliance.

POSIX 1003.2 Shell Standard.

Standards committees worked over the Bourne shell and added many features of the Korn shell (ksh88) and
C shell to define a standard set of features which all compliant shells must have.

On most systems, /bin/sh is now a POSIX compliant shell.
Korn shell and Bash are POSIX compliant, but have many features which go beyond the standard.
On Solaris, the POSIX/XPG4 commands which differ
slightly in behaviour from traditional SunOS commands are located in /usr/xpg4/bin

The "Bourne again" shell. Written as part of the GNU/Linux Open Source effort, and the default shell for Linux and
Mac OS-X. It is a functional clone of sh, with additional features to enhance interactive use,
add POSIX compliance, and partial ksh compatability.

A freeware functional clone of sh, with parts of ksh, bash and full POSIX compliance, and
many new interactive command-line editing features.
It was installed as the default shell on early MacOSX systems.